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- W3081784037 abstract "In the Metric Capacitated Covering (MCC) problem, given a set of balls ℬ in a metric space P with metric d and a capacity parameter U, the goal is to find a minimum sized subset ℬ' ⊆ ℬ and an assignment of the points in P to the balls in ℬ' such that each point is assigned to a ball that contains it and each ball is assigned with at most U points. MCC achieves an O(log |P|)-approximation using a greedy algorithm. On the other hand, it is hard to approximate within a factor of o(log |P|) even with β < 3 factor expansion of the balls. Bandyapadhyay et al. [SoCG 2018, DCG 2019] showed that one can obtain an O(1)-approximation for the problem with 6.47 factor expansion of the balls. An open question left by their work is to reduce the gap between the lower bound 3 and the upper bound 6.47. In this current work, we show that it is possible to obtain an O(1)-approximation with only 4.24 factor expansion of the balls. We also show a similar upper bound of 5 for a more generalized version of MCC for which the best previously known bound was 9." @default.
- W3081784037 created "2020-09-08" @default.
- W3081784037 creator A5001388244 @default.
- W3081784037 date "2020-01-01" @default.
- W3081784037 modified "2023-09-27" @default.
- W3081784037 title "Improved Bounds for Metric Capacitated Covering Problems" @default.
- W3081784037 doi "https://doi.org/10.4230/lipics.esa.2020.9" @default.
- W3081784037 hasPublicationYear "2020" @default.
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